Mismatch-Aware Adaptive Constraint Tightening for Bicycle-Model Trajectory Optimization

Autonomous racing overtaking requires balancing competitive performance with safety under nonlinear vehicle dynamics and real-time constraints. Model Predictive Control (MPC) combined with Control Barrier Functions (CBFs) provides a principled mechanism for certifying forward invariance of a safe set. However, commonly used fixed-decay discrete-time CBF formulations can become overly conservative in interactive racing scenarios, limiting overtaking performance and requiring manual tuning across track conditions. This paper proposes a hierarchical overtaking framework that explicitly separates maneuver-level decision making from safety-certified trajectory control, reducing conservatism while preserving safety. A high-level Mixed-Integer Quadratic Program (MIQP) resolves the combinatorial passing-side selection problem by selecting a feasible overtaking topology, while a nonlinear Frenet-frame MPC enforces vehicle dynamics and safety through embedded discrete-time CBF constraints. This decomposition isolates the combinatorial complexity of maneuver selection from the continuous trajectory optimization. To further mitigate the sensitivity of fixed-decay barrier constraints, a reinforcement learning policy adapts the discrete-time CBF decay parameter online, enabling context-dependent modulation of safety margins without directly controlling vehicle inputs. Simulation and scaled-hardware experiments show that no single fixed decay parameter achieves uniformly strong performance across tracks, whereas the adaptive strategy attains the highest aggregate success rate and consistently strong safety--performance trade-offs without per-track tuning, improving robustness to environment variation while maintaining safety constraint satisfaction in nominal operation.

Locating a vehicle and determining its orientation in an uncertain environment is a critical challenge in autonomous vehicle navigation and path planning. To address these challenges, a vehicle estimates its pose while depending on sensor data that offer noisy measurements. These uncertainties in pose quantities are expressed mathematically as a covariance matrix. The real-time computation of the covariance matrix is critical because of the non-linearity involved in the kinematic model. The challenge is thus to evaluate the evolution of the covariance matrix of a vehicle's discretized stochastic kinematics. The purpose of this study is to obtain a near-accurate evolution of the covariance matrix of the rear-wheel bicycle kinematic model under uncertainties in wheel displacement and steering angle. We used Taylor's series to linearize the nonlinear trigonometric functions and provided closed-form expectations of random variables with the required accuracy. Our analytical findings are in good agreement with those obtained from Monte-Carlo simulations. Our contribution is probably the first detailed closed-form presentation of the covariance matrix constituents of the vehicle under evaluation, which were previously reported either incorrectly or incompletely. These findings aid in identifying the potential and constraints of the discretized kinematic model as well as its stochastic analysis. The techniques presented here are useful for the simultaneous localization and odometry self-calibration of certain mobile robots and autonomous vehicles.

Autonomous systems are increasingly deployed in real-world environments, where they must achieve high performance while maintaining safety under state and input constraints. Although Model Predictive Control (MPC) provides a principled framework for constrained optimal control, guaranteeing safety beyond its finite planning horizon remains a fundamental challenge. In this work, we augment MPC with a safety value function-based terminal constraint that enforces membership in a control-invariant safe set at the end of each planning horizon. This formulation enables real-time synthesis of trajectories that are both high-performing and provably safe. We show that, under an exact safety value function and a feasible initialization, the proposed MPC scheme is recursively feasible, thereby ensuring persistent safety. In contrast to traditional terminal set constructions that rely on local linearizations or conservative approximations, our approach incorporates a reachability-based safety value function for terminal constraints, yielding less conservative and more expressive safety guarantees. We validate the proposed framework through simulation and hardware experiments on a Flexiv Rizon 10s manipulator. Results demonstrate improved constraint satisfaction and robustness compared to standard state-constrained MPC and reactive safety filtering, while maintaining competitive task performance. The full implementation and experiments are available on the project website.